Theory and Modern Applications
Table 8 Pointwise absolute errors in the maximum norm and computed rates of convergence versus the number of sub-intervals N in Example 4.3 as we set \(\alpha _{1} = 0.4\), \(\alpha _{2} = 1.7\), \(m=10\)
N | Newton’s method | Halley’s method | ||||||
|---|---|---|---|---|---|---|---|---|
\(s_{0}=0.2\) | \(s_{0}=1.0\) | \(s_{0}=0.2\) | \(s_{0}=1.0\) | |||||
Max. error | Rate | Max. error | Rate | Max. error | Rate | Max. error | Rate | |
10 | 1.73E−04 | – | 1.73E−04 | – | 1.19E−05 | – | 1.19E−05 | – |
20 | 6.85E−05 | 1.338 | 6.85E−05 | 1.338 | 3.97E−06 | 1.578 | 3.97E−06 | 1.578 |
40 | 2.07E−05 | 1.727 | 2.07E−05 | 1.727 | 6.62E−07 | 2.586 | 6.62E−07 | 2.586 |
80 | 5.63E−06 | 1.877 | 5.63E−06 | 1.877 | 9.28E−08 | 2.834 | 9.28E−08 | 2.834 |
160 | 1.47E−06 | 1.942 | 1.47E−06 | 1.942 | 1.22E−08 | 2.926 | 1.22E−08 | 2.926 |
320 | 3.74E−07 | 1.971 | 3.74E−07 | 1.971 | 1.56E−09 | 2.966 | 1.56E−09 | 2.966 |